How can I fit 3-D scatter points with value?

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I have an output file from a fluent simulation. The output file contains the coordinates of each of the nodes and the pressure value of each node. In other words, each point has its coordinate (theta, r, z) and its pressure value p. Is there a way I could fit these scatter points and output an expression p(theta,r,z)?
Thank you,

Accepted Answer

Abdolkarim Mohammadi
Abdolkarim Mohammadi on 7 Aug 2020
Edited: Abdolkarim Mohammadi on 7 Aug 2020
If your model for the relationship between (theta, r, z) triplets and the pressure is linear, use regress. Otherwise, use lsqcurvefit or nlinfit. You cannot use the curve fitting app (cftool) because it only supports up to two independent variables.
Abdolkarim Mohammadi
Abdolkarim Mohammadi on 7 Aug 2020
(1) When you split apart values of theta, you are treating it as a moderator variable. In other words, you are assuming that theta does not directly affect pressure; it is just affecting the model (r,z)=>p. This is in contrast with the assumption of the direct effect of theta in the model (r,p,theta)=>p.
(2) As I mentioned in my previous comment, interpolation does not produce equation. It just interpolates between your data points to fill the gaps between datapoints. For example, if you have only two data points of (x=0,y=0) and (x=1,y=2) then you create interpolation and evaluate the interpolation at x=0.5, then it returns y=1, which is the intermediate between your points.
(3) You should not judge the quality of interpolation models based on . Any type of interpolation will always lead to . It's because they do not produce error at datapoints.

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